Giải pt: $\sqrt{x+5-4\sqrt{x+1}}+\sqrt{x+5+4\sqrt{x+1}}=4$

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$\\$ `sqrt{x+5-4sqrt{x+1}}+sqrt{x+5+4sqrt{x+1}}=4`

$\\$ Điều kiện: `x>=-1`

$\\$ `<=>sqrt{x+1-4sqrt{x+1}+4}+sqrt{x+1+4sqrt{x+1}}=4`

$\\$ `<=>sqrt{(sqrt{x+1}-2)^2}+sqrt{(sqrt{x+1}+2)^2}=4`

$\\$ `<=>|sqrt{x+1}-2|+|sqrt{x+1}+2|=4`

$\\$ TH1: `x>=3`

$\\$ `=>|sqrt{x+1}-2|+|sqrt{x+1}+2|=4`

$\\$ `<=>sqrt{x+1}-2+sqrt{x+1}+2=4`

$\\$ `<=>2sqrt{x+1}=4`

$\\$ `<=>sqrt{x+1}=2`

$\\$ `<=>x+1=4`

$\\$ `<=>x=3`(Thỏa mãn)

$\\$ TH2:`-1<=x<3`

$\\$ `=>|sqrt{x+1}-2|+|sqrt{x+1}+2|=4`

$\\$ `<=>2-sqrt{x+1}+sqrt{x+1}+2=0`

$\\$ `<=>4=0`(Vô lý)

$\\$ Vậy `S={3}`